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# Geometrical Modelling in Graphics (Course Materials)

Lecture Monday 8:10 M-XII Exercise Tuesday 13:10 M-XII

No make-up exams will be given for missed tests. All the assignments should be turn in by the designated due date. To pass this course all the course requirements must be SATISFACTORILY completed > 30% of each problem set. Programming, modelling projects and oral exam.

## What you Need to Pass

• Attend lessons. One missed +0 points. 2 missed 0 points, 3 missed 0 points, 4 and more is Fx.
• Programming, modelling project with production and exercise (mandatory, 50 points). Submission after deadline -50%.
• All programming is checked with deadlines during the exercises.
• Pass oral/written exam: (+20 points) If you feel you are better, convince me !
• Summary
• Attendance = 0 or -100 (Fx)
• Projects = +50..0
• Oral/written exam = +50..0
```   A = 92-100
B = 84-91
C = 76-83
D = 68-75
E = 60-67
Fx = 0-59
```

### Oral Examination

To the oral examination all the above requirements must be SATISFACTORILY completed. Random lecture topic will be selected and presented by a student after written preparation.

• Michael Henle, "A Combinatorial Introduction to Topology"
• J. O'Rourke, "Computational Geometry in C"

### Lesson00 "Introduction to Geometry Modelling"

• Lecture schedule
• "Terms and conditions" of this lecture
• Lecture notes: lesson00.pdf

### Lesson01 "Polygonal meshes, Winged Edge, Quad Edge, DCEL"

• 2D manifold
• Polygonal meshes
• Winged Edge
• Double Connected Edge List
• Lecture notes: lesson01.pdf

### Lesson02 "Polygonal Mesh Properties"

• Normal, curvature, object interior
• Descriptors
• Bounded volume
• Lecture notes: lesson02.pdf

### Lesson03 "Polygonal Mesh Simplification"

• Mesh simplification algorithm
• Terrain visualisation
• Progressive meshes
• Lecture notes: lesson03.pdf

### Lesson04 "Polygonal Mesh Smoothing"

• Polygon and mesh smoothing with subdivision
• Catmull-Clark subdivision, Modified Butterfly subdivision
• Mesh Laplacian smoothing
• Lecture notes: lesson04.pdf

### Lesson05 "Polygonal Mesh Repairing"

• Polygon and mesh smoothing with subdivision
• Delaunay triangulation
• Triangulation in 3D
• Filling holes in meshes
• Volumetric mesh repair
• Lecture notes: lesson05.pdf

### Lesson06 "Curves"

• Polynomial curves
• Spline curves
• Rational curves
• Implicit curves
• Lecture notes: lesson06.pdf

### Lesson07 "Surfaces"

• Polynomial surfaces
• Spline surfaces
• Rational surfaces
• Implicit surfaces
• Lecture notes: lesson07.pdf

### Lesson08 "Volumes"

• Distance function
• Voxelization: Mesh voxelization, Implicit surface voxelization
• Distance transforms
• Fast marching method
• Visualization
• Lecture notes: lesson08.pdf

### Lesson09 "Point Clouds"

• Point cloud sources
• K-nearest neighbor search on Kd-tree
• Normal estimation
• Registration
• Visualization
• Lecture notes: lesson09.pdf

### Lesson10 "Surface Reconstruction"

• Implicit reconstruction
• Power crust mesh reconstruction
• Parameteric reconstruction
• Lecture notes: lesson10.pdf

# EXERCISES

Your presence at the seminar is mandatory. Exercise projects are done in Unity3D with C# language. We load the 3D objects with Assimp library .NET version.

### Exercise 02"Assimp library in Unity3D”

• Object import from a file, filling the DCEL structure.

### Exercise 03 "Triangle selection”

• Select a triangle with a mouse click, find and visualise the neighbouring triangles. Generate the DCEL structure for a sphere.

### Exercise 04 "Compiler in Unity”

• Unity compiler, object simplification based on shortest edge.

### Exercise 05 "Object simplification”

• Object simplification based on shortest edge. Edge collapsing to a vertex and new vertex position.

### Exercise 06 "Object simplification”

• Object simplification based on shortest edge. DCEL structure update in the neighbourhood of deleted edge.

### Exercise 07 "Loop subdivision”

• Loop subdivision, position of new vertices.

### Exercise 08 "Loop subdivision”

• Vertex connection into a triangle and filling the DCEL structure.

### Exercise 09 "Volume representation with voxels”

• Regular grid representation of a sphere and a cube and filling the structure.

### Exercise 10 "Marching cubes algorithm”

• Selection of voxel configuration at voxel position. Linear interpolation along the voxel edges.

### Exercise 11 "Marching cubes algorithm”

• Selection of voxel configuration at voxel position. Linear interpolation along the voxel edges. Tutorial is here

### Exercise 12 "Marching cubes algorithm”

• Triangle generation for each voxel. DCEL structure generation for newly generated triangles. Tutorial is here

### Exercise 13 "Marching cubes algorithm”

• Trilinear interpolation, object intersection.

--- Prvá domáca úloha: Half-edge štruktúra, vytvorenie štruktúry z naimportovaného súboru (klávesa D pre duck.dae), vytvorenie štruktúry pre kocku a sféru (na stlačenie kláves C a S), zisťovanie susedných prvkov, vizualizácia.

• Termín odovzdania je 15.3.2017. Maximálny bodový zisk za úlohu je 15 bodov.

--- Druhá domáca úloha: Prerozdeľovací Loopov algoritmus a zjednodšovací edge-collapse algoritmus podľa najkratšej hrany na half-edge štruktúre. Na tlačítko L sa vykoná jeden krok Loopovho algoritmu na aktuálnom modely (aj s pravidlami pre hranicu), na tlačítko E sa vykoná kolaps aktuálne najkratšej hrany, na tlačítko R sa odstráni naraz 50% najkratších hrán. Projekt musí obsahovať ďalší model s hranicou na otestovanie algoritmov.

• Termín odovzdania je 19.4.2017. Maximálny bodový zisk za úlohu je 15 bodov.

--- Tretia domáca úloha: Štruktúra pre vzdialenostné pole na pravidelnej mriežke. Prevod základných objektov a objektov z implicitnej reprezentácie do volumetrickej (kocka pri stlačení F1, sféra pri stlačení F2 a srdce pri stlačení F3). Prienik dvoch objektov (sféry a srdca) vo volumetrickej reprezentácii po stlačení F4. Marching cubes (vytvorenie DCEL štruktúry z pravidelnej volumetrickej mriežky).

• Termín odovzdania je 24.5.2017. Maximálny bodový zisk za úlohu je 20 bodov.